NONPARAMETRIC TESTS FOR COMPARING SURVIVAL DATA WITH NONPROPORTIONAL HAZARDS: EXPLORATION OF A NEW WEIGHT FUNCTION

For survival data with nonproportional hazards, the weighted log-rank tests with a proper weighting function are expected to be more sensitive than the simple log-rank statistics for comparing survival data with random effects. A series of simulations were carried out to investigate how much better the weighted log-rank test performs under these situations. The nonproportional hazards data were generated by changing the hazard ratios and piecewise exponential functions. Our Monte Carlo simulation study shows the test with a newly developed weight function has an overall better sensitivity (statistical power) than the simple log-rank test and Harrington-Fleming's weighted log-rank test in detecting the difference between two survival distributions when populations become more homogeneous as time progresses (early difference). For the datasets with middle difference, the test with the new weight function has better sensitivity than that of Harrington-Fleming's weighted log-rank test, similar to that of the simple-log rank test. For late difference, all three tests have similar sensitivity. The new weight function can be used in testing the survival data with nonproportional hazards in public health relevance applications